Exponents ...

Hello,

I'm just learning about exponents and having a trouble totally understanding them. My parents signed up and paid a year's subscription for a website that allows me to download tests in math with an answer key because it is a subject that neither of them can help me with. Being bad at math runs in the family . Anyway, I have downloaded some tests on adding and subtracting exponents and it is helping me understand a bit more. But I am confused about some of the questions I have got wrong the answers on the answer key do not make sense to me. I am wondering if there are perhaps the odd mistake on the answer keys. Could someone help me with the following ...

The question:

1. (c^5 + c^2) x (c^6 x c^8)

My answer: c^7 x c^14
= c^21

Key answer: c^19 + c^16

My answer is possibly wrong but I have not got a clue about the key answer.

2. 7^7 + 7^7 x 7^7 x 7^7

My answer: 7^14 x 7^10
= 7^24

Key answer: 7^7 + 7^17

My answer is possibly wrong but I have not got a clue about the key answer.

A general question. In addition if the base is the same do you add the exponents and leave the base as is or do you figure out the exponents meaning the answer to this question should be...

I'm just learning about exponents and having a trouble totally understanding them. My parents signed up and paid a year's subscription for a website that allows me to download tests in math with an answer key because it is a subject that neither of them can help me with.

Out of curiosity, what website was it?

Originally Posted by walrus

1. (c^5 + c^2) x (c^6 x c^8)

My answer: c^7 x c^14
= c^21

Key answer: c^19 + c^16

There is an addition term in the first parenthesis, so we should expect at least two terms in our final answer.

Your problem was that you treated that first addition sign as a multiplication sign and added all of the exponents together.

Originally Posted by walrus

2. 7^7 + 7^7 x 7^7 x 7^7

My answer: 7^14 x 7^10
= 7^24

Key answer: 7^7 + 7^17

My answer is possibly wrong but I have not got a clue about the key answer.

Either the answer key or your representation of the problem is wrong.

Originally Posted by walrus

A general question. In addition if the base is the same do you add the exponents and leave the base as is or do you figure out the exponents meaning the answer to this question should be...

eg. 6^3 + 6^2 + 6^2
= 6^9

or

6 x 6 x 6 + 6 x 6 + 6 x 6
=216 + 36 + 36
=288

You only add the exponents when like bases are multiplied together. When they are added, you cannot do much for simplification purposes.